Tag: maths

Questions Related to maths

At $5:20$ the angle formed between the two hands of a clock is:

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. obtuse angle

  2. right angle

  3. acute angle

  4. None of the above

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Correct Option: C
Explanation:

At $5:20$ the angle formed between the two hands of a clock will be less than $90^o$.

So, it is an acute angle.

What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past $4$?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $\dfrac{\pi}{3}$

  2. $\dfrac{\pi}{4}$

  3. $\dfrac{\pi}{6}$

  4. None of the above

Show answer
Correct Option: B
Explanation:

In the clock the angle between each hour division will be $\dfrac { 360 }{ 12 } =30^{o}$. 

Now here at $4:30$, the hour hand will be along AB which is the angle bisector between $4$ and $5$ and the minute hand will be along AC,
The angle between them will be $=30+15=45$,in radians $\dfrac { \pi  }{ 4 }$ 

Hence, B is correct.

At what time is the angle between the hands of a clock equal to $30^{o}$ ?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $1:00$

  2. $11:00$

  3. $2:00$

  4. $12:00$

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Correct Option: A,B
Explanation:

A clock is a circle made of $360^\circ$, and that each hour represents an angle and the separation between them is $\dfrac{360^\circ}{12}=30^\circ$


Hence, 
At $1:00$ the angle between the hands is $30^\circ$, minute hand pointing at 12 and hour hand at 1.

Similarly
At $11:00$ the angle between the hands is $30^\circ$

At $2:00$ the angle between the hands is $60^\circ$

At $12:00$ the angle between the hands is $0^\circ$

How many times between $6:00$ am and $6:00$ pm, do the hands of a clock make a straight line 

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $9$

  2. $10$

  3. $11$

  4. $12$

Show answer
Correct Option: C
Explanation:
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours.

 (Because between 5 and 7 they point in opposite directions at 6 o'clock only).

So between $6:00$ am to $6:00$ pm ($12$ hours), $11$ times hands of a clock make a straight line.

How many times in a day, do the hands of a clock make a right angle ?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $21$

  2. $22$

  3. $42$

  4. $44$

Show answer
Correct Option: D
Explanation:

There will be $2$ times per hour when the angle between minute and hour hand is $90^\circ$

Total of $22$ times in $12$ hours.
$\therefore$ In $24$ hours, $22\times 2=44$ times the angle between minute and hour hand is $90^\circ$.

At 2:15 o'clock, the hour and minute hands of a clock form an angle of:

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $30^{\circ}$

  2. $5^{\circ}$

  3. $22\dfrac{1}{2}{\circ}$

  4. $7\dfrac{1}{2}{\circ}$

Show answer
Correct Option: C
Explanation:
   $\underset { \downarrow  }{ \underline { 2 }  } <2:15<\underset { \downarrow  }{ 3 } $' $O$ clock
$\left( { 60 }^{ 0 } \right) $             $\left( { 90 }^{ 0 } \right) $
when minute hand rotates $15$ min hour hand rotate $\dfrac { 15 }{ 60 } \times { 30 }^{ 0 }={ 7.5 }^{ 0 }$
So, angle at $2:15$ is $=\left( { 90 }^{ 0 }-\left( { 60 }^{ 0 }+{ 7.5 }^{ 0 } \right)  \right) ={ 22.5 }^{ 0 }$

A particle starts from a point $z _0= I + i$, where $i
=\sqrt{-1}$ It moves horizontally away from origin by $2$ units and then
vertically away from origin by $3$ units to reach a point$ z _1$. From $z _1$
particle moves $\sqrt{5}$ units in the direction of $2\hat i + \hat j$ and
then it moves through an angle of $\cos e{c^{ - 1}}\sqrt 2 $ in anticlockwise
direction of a circle with centre at origin to reach a point $z _2$ . The arg $z _2$ is given by

maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

  1. ${\sec ^{ - 1}}2$

  2. ${\cot ^{ - 1}}0$

  3. ${\sin ^{ - 1}}\left( {\dfrac{{\sqrt 3 - 1}}{{2\sqrt 2 }}} \right)$

  4. ${\cos ^{ - 1}}\left( {\dfrac{{ - 1}}{2}} \right)$

Show answer
Correct Option: B

The number of solution of $z^2 + \bar{z} = 0$ is

maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

  1. $5$

  2. $4$

  3. $2$

  4. $3$

Show answer
Correct Option: B
Explanation:
Let $z=x+iy$.
Now,
$z^2+\overline{z}=0$
or, $x^2-y^2+2ixy+(x-iy)=0$
or, $(x^2-y^2+x)+i(2xy-y)=0$
Now comparing the real and imaginary part both sides we get,
$x^2-y^2+x=0$.....(1) and $2xy-y=0$.....(2).
From (2) we get, $x=\dfrac{1}{2}$ or $y=0$.
Now $x=\dfrac{1}{2}$ gives from (1) we get, $y=\pm \dfrac{\sqrt{3}}{2}$.
And $y=0$ gives from (1) we get, $x=0, 1$.
So the solution s are $(0,0), (1,0), \left(\dfrac{1}{2},\pm \dfrac{\sqrt{3}}{2}\right)$.
So we have $4$ solutions.

If $z \neq 0$, then $ \overset{100}{\underset{0}{\int}}arg(-|z|)dx =$

maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

  1. $0$

  2. Not defined

  3. $100$

  4. $100\pi$

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Correct Option: A

The complex no. $\dfrac{1+2i}{1-i}$ lies in which quadrant of the complex plane

maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

  1. first

  2. second

  3. third

  4. fourth

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Correct Option: B